Well, you can pass her by at school and if she looks at you, say "hi" with a smile and flank in s "you look great/fine today!" or "Hi, Sandy, and you look great today!" You know, it's hard to script, but say it in some way that's natural to you so it doesn't sound stalkish, not-you, or scripted ... do it in a straightforward and happy way. It's important to say it passing-by, or just smile and keep a quick conversation with her for like 10 seconds. Otherwise, she might get uncomfortable and feel like she needs to respond. It's very possible she's not been in a situation like that before. I found that this works pretty well in those situations, provided that you're a kinda laid back and relaxed person. I'm not the kinda guy that meets people out in bars and stuff, so I know what you mean about talking to somebody in school.
Looking for conversational topics, I'm not sure what's good and bad. It depends on the person. About her friends, do give them smiles and acknowledgement also. Involve them in conversations. Because when you do that, her friends will start talking to her about you, and that's a good thing. They'll say stuff like you're nice and they'd date you and so, and that leads to her wanting to see you a bit more.
Again, start off with some of those quick compliments. Pass her by and say some so she feels good. And finally, do get her e-mail address FROM HER ... ask her if she's got e-mail and what it is and stuff. I used that trick in school once that is was for some "homework assignments", but nowadays I'm more straightforward. You know, "I like talking to you, you're a real interesting person!" and get it through those channels. No hidden agendas. It's "I want you get to know you" and no beating around the bush.
NOTE: do compliment on personality and intelligence. And ... patience is a virtue.